Walking down the path to the surreal numbers part 2

I’ve got less time to write today because of a family trip, but the videos below show part 2 of our Family Math project about “checker stacks” and the surreal numbers.

The first part of the project is here:

Walking down the path to the surreal numbers

and we are following Jim Propp’s blog post about the surreal numbers which is here:

Jim Propp’s “The Life of Games”

The first thing we looked at today was “deep blue” stack. The surprise about this piece in the game of checker stacks is that its value appears to be positive infinity.

Next we quickly looked at the “deep red” piece and then looked at a blue + deep red stack whose value is pretty surprising. It was great to hear the ideas that the kids had about this stack.

Next we moved on to study the “deep purple” piece. This piece is pretty mysterious. I thought pretty hard about how to explain the value of this piece to the boys, but didn’t really come up with any good ideas. Instead we spent about 10 minutes exploring its value. That was a great conversation, but we never did quite get to the value of 2/3 that Propp gives in his blog. I’m ok with that outcome, though – I felt the conversation about the possible values was really great.

So, sorry for the quick write up of this 2nd project about the surreal numbers. I’m really happy to have seen Jim Propp’s blog and think there’s got to be a great way to use checker stacks for a neat math project for kids.

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